A note on the extremality of the disordered state for the Ising model on the Bethe lattice

Authors

Ioffe, Dmitry

Keywords

Bethe lattice, FK representation, Ising model

Abstract

We give a simple proof that the limit Ising Gibbs measure with free boundary conditions on the Bethe lattice with the forward branching ratio k ≥ 2 is extremal if and only if β is less or equal to the spin glass transition value, given by tanh(βSGc) = 1/√k.